Former Texas Sen. Kay Bailey Hutchison said though the events following the Boston bombings will not have an impact on the progress of immigration reform, the week-long search for the suspects involved should indicate to immigration reformers to be more aware of an immigrant’s history prior to coming into the United States.

“I think we need to be looking at the criteria for people that we allow to become permanent residents and legal immigrants in this country,” she told MSNBC’s Alex Witt on Sunday. “And I think background is very important, and so I think that is a point that fortunately we are in the midst of having the opportunity to address.”

She said the incident should serve as a “warning flag” for Congress that can be considered in the overall discussion of immigration reform.

“We want the people who come in here not to be carrying the baggage of wanting to harm innocent Americans because of some skewed position on what we are and who we are and the freedom that we love,” Hutchison said.

As Congress continues its debate on immigration reform, including a Senate Judiciary hearing today, some lawmakers have used the bombings as a way to drive home their own talking points on immigration reform. Dzhokhar Tsarnaev and his older brother Tamerlan Tsarnaev where Chechen and had come to the U.S. with their family when they were younger. Officials say 26-year-old Tamerlan Tsarnaev had visited Chechnya where he may have forged ties with al Qaeda.

Several legislators, including Texas Rep. Mike McCaul, chair of the House Homeland Security Committee, questioned whether the FBI should have kept better tabs on elder brother after questioning him years ago. Hutchison said it’s too soon to rally criticism at investigators.

“I can’t say anything critical about them right now, because I think that it’s a huge relief that so far these two are gone. But if they are connected to other terrorist organizations, and if they’re helping to ferment that, then I think we need to be very vigilant,” Hutchison said.

On Sunday, several Republicans called for Dzhokhar Tsarnaev to be tried as an enemy combatant. Hutchison agreed the 19-year-old should be labeled as an enemy combatant and also sided with those who say Tsarnaev should not be allowed his Miranda rights. Officials have expressed interest in using the public safety exception to Miranda rights, which can be used to gather important information from suspects if it’s believe they hold information that’s detrimental to the public’s safety.

“I think we should be leaning on that side rather than what I think is appearing to happen is that the prosecutors are kind of saying, ‘No, we’re going the route of giving him his Miranda rights.’ I that is not a good thing to be saying right now, or indicating right now. We need to know what this young man knows that could help us protect American lives right now,” she said.